B. Chilton and R. Whorf have studied stellations of the triakis tetrahedron (Wenninger 1983, p. 36). Whorf has found 138 stellations, 44 of which are fully symmetric and 94 of which are enantiomorphs (Wenninger 1983, p. 36).
Applying Miller's rules (the same as for the icosahedron stellations) to this solid, the stellation software Great Stella finds 188 stellations (including the original model), 52 of them reflexible and 136 of them chiral (Webb).
The stellation diagram showing the lines of intersections of nonparallel face planes with the plane of one face is shown above. Note that the actual diagram differs in the height and angle of the top "spike" compared to the apparently slightly erroneous figure appearing in Wenninger (1989, p. 37, Fig. 27).
